Math 252: Abstract Algebra II

Spring 2012

 

Course Info:

 

Syllabus:

[PDF] Syllabus

 

Homework:

[PDF] Homework Submission Guidelines

[TeX] [PDF] Homework Template

[PDF] HW #1 (due 27 January 2012)

[PDF] HW #2 (due 3 February 2012); updated 30 January 2012

[PDF] HW #3 (due 10 February 2012)

[PDF] HW #4 (due 17 February 2012); updated 16 February 2012

[PDF] HW #5 (due 24 February 2012)

[PDF] HW #6 (due 16 March 2012); updated 16 March 2012

[PDF] HW #7 (due 23 March 2012); updated 19 March 2012

[PDF] HW #8 (due 30 March 2012)

[PDF] HW #9 (due 6 April 2012)

[PDF] HW #10 (due 13 April 2012)

[PDF] HW #11 (due 20 April 2012)

[PDF] HW #12 (due 27 April 2012); typo fixed 26 April 2012

 

Readiness Problems:

The readiness problem is due on the same day as the row in which it appears. Problem 3.5.2 means in section 3.5, exercise 2.

Euclidean domains, PIDs, and UFDs, and polynomial rings
1 18 Jan(W) 8.1: Euclidean domains
2 20 Jan(F) 8.1 8.1.1(b)
3 23 Jan(M) 8.2: Principal ideal domains 8.1.4(a)
4 25 Jan(W) 8.3: UFDs 8.2.3
5 27 Jan(F) 7.5: Rings of Fractions 8.3.5(a)
6 30 Jan(M)9.2, 9.5: Polynomial rings over fields I, II 7.5.4, 8.1.A
7 1 Feb(W) 9.4: Irreducibility criteria 9.2.A
Modules
8 3 Feb(F) Linear algebra crash course (11.1) 9.4.1, 9.4.2(a)
9 6 Feb(M) Linear algebra crash course (11.1) 11.1.1
10 8 Feb(W) 10.1: Basic definitions and examples (Worksheet)
11 10 Feb(F) 10.1 10.1.1
12 13 Feb(M) 10.2 : Quotient modules and module homomorphisms 10.1.15
13 15 Feb(W) 10.2 10.2.1
14 17 Feb(F) 10.2 10.2.3
20 Feb(M) No class, Presidents Day
15 22 Feb(W) 10.3: Generation of modules, direct sums, and free modules
Vector spaces
16 24 Feb(F) 11.2: The matrix of a linear transformation 10.3.23
17 27 Feb(M) 11.2 11.2.1
18 29 Feb(W) 11.3: Dual vector spaces 11.2.2
19 2 Mar(F) 11.4: Determinants 11.3.2(a)
5-9 Mar(M-F) No class, spring break
Modules over PIDs
20 12 Mar(M) 12.1: Basic theory
21 14 Mar(W) 12.1 12.1.1(a)
22 16 Mar(F) 12.2: Rational canonical form 12.1.5
23 19 Mar(M) 12.2 12.2.8
24 21 Mar(W) 12.3: Jordan canonical form 12.2.9 (just the two easy ones!)
Bring your laptop!
Field theory
25 23 Mar(F) 13.1: Basic theory of field extensions 12.3.5
26 26 Mar(M) 13.1 13.1.1
27 28 Mar(W) 13.2: Algebraic extensions 13.1.3
28 30 Mar(F) 13.2 13.2.1
29 2 Apr(M) 13.3: Classical straightedge and compass constructions 13.2.3
30 4 Apr(W) 14.1: Basic definitions 13.3.2
Galois theory
31 6 Apr(F) 13.4: Splitting fields and algebraic closures,
13.5: Separable and inseparable extensions
14.1.2, 14.1.3
32 9 Apr(M) 14.1 13.4.1
33 11 Apr(W) 14.2: The fundamental theorem of Galois theory 14.1.4
34 13 Apr(F) 14.2 14.2.3
35 16 Apr(M) 14.2 14.2.4
Finite fields and insolvability of the quintic
36 18 Apr(W) 14.3: Finite fields 14.2.12
37 20 Apr(F) 14.3 14.3.2
38 23 Apr(M) 14.5: Cyclotomic extensions and abelian extensions over QQ 14.3.5
39 25 Apr(W) 14.7: Solvable and radical extensions 14.5.3
40 27 Apr(F) 14.7 14.7.1
41 30 Apr(M) 14.6: Galois groups of polynomials 14.7.12
42 2 May(W) 14.6

 

Links:

There are additional resources on the 252 Spring 2008 website.